That wouldn't be very ideal for recording would it? Wouldn't you choke the sound quite a bit by closing the top?
Well, nobody says you HAVE to close the top when close miking. In fact if you're using regular mic stands/booms to close mic, you have to leave the lid open to make room for the booms to come in.
But the main thing is when close miking, you're not getting the full-developed far field sound of the instrument anyway. This is true not just piano, but of
acoustic guitar and other resonant acoustic instruments as well. That doesn't mean that it won't sound good, most of us use near-field miking on guitars and violins all the time, and - in anything short of a great-sounding auditorium or live room - close miking on pianos usually sounds better than far-miking in a lousy-sounding room.
Closing the lid does affect close-miking somewhat, but nowhere near to the degree as it might sound from the outside.
I prefer leaving the lid open, myself, and usually have to because I do not yet have one of those Earthworks contraptions, but often times one might be concerned about bleed from other instruments - especially because the piano is so relatively quiet. in such cases closing the lid halfway or all the way, or draping blankets over the opening may be desired for the isolation properties.
G.